Based on the graph of the given limit of a function, the value for which [tex]\lim_{x \to a} g(x)[/tex] doesn't exist is equal to -3.
What is a limit?
A limit can be defined as a numerical value which a function approaches (output) as the input value approaches other values. In Mathematics, limits are typically used to determine the following:
For the right-hand limit, we have:
[tex]\lim_{x \to -3^{+}}[ -3 + 1] = -2[/tex]
For the right-hand limit, we have:
[tex]\lim_{x \to -3^{-}} [-3 - 1] = -4[/tex]
By critically observing the graph of the given limit of a function, we can logically deduce that -3 is the value for which [tex]\lim_{x \to a} g(x)[/tex] doesn't exist because the right-hand limit and left-hand limit are not the same (different).
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